Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 1301 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 64 } = 1 $$ | 1 |
| 1302 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 144 } + \dfrac{ \left( y - 1 \right)^2}{ 121 } = 1 $$ | 1 |
| 1303 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ 9 y^2}{ 9 } = 1 $$ | 1 |
| 1304 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 81 } + \dfrac{ y^2}{ 256 } = 1 $$ | 1 |
| 1305 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 55 } + \dfrac{ y^2}{ 200 } = 1 $$ | 1 |
| 1306 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 100 } + \dfrac{ y^2}{ 200 } = 1 $$ | 1 |
| 1307 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 25 \left( x - 1 \right)^2}{ 1 } + \dfrac{ 4 \left( y + 1 \right)^2}{ 1 } = 1 $$ | 1 |
| 1308 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 25x^2 + 4y^2 = 71 $$ | 1 |
| 1309 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 25 \left( x - 1 \right)^2}{ 4 } + \dfrac{ 4 \left( y + 1 \right)^2}{ 25 } = 1 $$ | 1 |
| 1310 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 144 } + \dfrac{ \left( y + 6 \right)^2}{ 169 } = 1 $$ | 1 |
| 1311 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ \left( y - 1 \right)^2}{ 4 } = 1 $$ | 1 |
| 1312 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 25 } + \dfrac{ \left( y + 6 \right)^2}{ 49 } = 1 $$ | 1 |
| 1313 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 789 }{ 100 } \right)^2}{ \frac{ 3 }{ 250 } } + \dfrac{ \left( y - \frac{ 199 }{ 20 } \right)^2}{ \frac{ 17 }{ 1000 } } = 1 $$ | 1 |
| 1314 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 17 }{ 2 } } + \dfrac{ y^2}{ 7 } = 1 $$ | 1 |
| 1315 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \frac{ 17 }{ 2 }x^2 + 7y^2 = 36 $$ | 1 |
| 1316 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \frac{ 17 }{ 2 }x^2 + 7y^2 = 1 $$ | 1 |
| 1317 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 1 |
| 1318 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 25 } + \dfrac{ \left( y + 5 \right)^2}{ 16 } = 1 $$ | 1 |
| 1319 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + 4y^2 = 36 $$ | 1 |
| 1320 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 12 } + \dfrac{ \left( y + 3 \right)^2}{ 36 } = 1 $$ | 1 |
| 1321 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 12 } = 1 $$ | 1 |
| 1322 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 16 } + \dfrac{ \left( y + 4 \right)^2}{ 12 } = 1 $$ | 1 |
| 1323 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 12 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 1324 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 12 } = 1 $$ | 1 |
| 1325 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + 16y^2 = 1 $$ | 1 |
| 1326 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 16 } + \dfrac{ \left( y + 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 1327 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 16 } + \dfrac{ \left( y - 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 1328 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 27 } + \dfrac{ y^2}{ 36 } = 1 $$ | 1 |
| 1329 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 4 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 1330 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 25 } + \dfrac{ \left( y - 1 \right)^2}{ 16 } = 1 $$ | 1 |
| 1331 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 9 \left( x - 1 \right)^2}{ 96 } + \dfrac{ 16 \left( y + 1 \right)^2}{ 96 } = 1 $$ | 1 |
| 1332 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 72 } + \dfrac{ y^2}{ 36 } = 1 $$ | 1 |
| 1333 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 6400 } + \dfrac{ y^2}{ 3600 } = 1 $$ | 1 |
| 1334 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 6 \left( x + 7 \right)^2}{ 11 } + \dfrac{ 4 \left( y + 2 \right)^2}{ 1 } = 1 $$ | 1 |
| 1335 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 6 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 1 |
| 1336 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 10 } + \dfrac{ y^2}{ 18 } = 1 $$ | 1 |
| 1337 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 18 } + \dfrac{ y^2}{ 28 } = 1 $$ | 1 |
| 1338 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ \frac{ 707 }{ 1000 } } = 1 $$ | 1 |
| 1339 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 2 } + \dfrac{ y^2}{ 4 } = 1 $$ | 1 |
| 1340 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 289 } + \dfrac{ y^2}{ 226 } = 1 $$ | 1 |
| 1341 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y - 8 \right)^2}{ 25 } = 1 $$ | 1 |
| 1342 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 9 } + \dfrac{ \left( y + 8 \right)^2}{ 64 } = 1 $$ | 1 |
| 1343 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 8 \right)^2}{ 25 } + \dfrac{ \left( y + 7 \right)^2}{ 9 } = 1 $$ | 1 |
| 1344 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 9y^2 = 1 $$ | 1 |
| 1345 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 25 } = 1 $$ | 1 |
| 1346 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 4 } + \dfrac{ \left( y - 7 \right)^2}{ 9 } = 1 $$ | 1 |
| 1347 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 1348 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1.0001 } + \dfrac{ y^2}{ 0 } = 1 $$ | 1 |
| 1349 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ y^2}{ \frac{ 7 }{ 2 } } = 1 $$ | 1 |
| 1350 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 125 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
